New bounds on the total-squared-correlation of quaternary signature sets and optimal designs

Authors:
Ming Li;N. Batalama;Dimitris A. Pados;John D. Matyjas
Affiliations:
Department of Electrical Engineering, State University of New York at Buffalo, Buffalo, NY;Department of Electrical Engineering, State University of New York at Buffalo, Buffalo, NY;Department of Electrical Engineering, State University of New York at Buffalo, Buffalo, NY;Air Force Research Laboratory, RIGE, Rome, NY
Venue:
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Year:
2009

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Abstract

We derive new bounds on the total squared correlation (TSC) of quaternary (quadriphase) signature/sequence sets for all lengths L and set sizes K. Then, for all K, L, we design minimum-TSC optimal sets that meet the new bounds with equality. Direct numerical comparison with the TSC value of the recently obtained optimal binary sets shows under what K, L realizations gains are materialized by moving from the binary to the quaternary code-division multiplexing alphabet. On the other hand, comparison with the Welch TSC value for real/complex-field sets shows that, arguably, not much is to be gained by raising the alphabet size above four for any K, L.